I know this is splitting hairs, but it's a 2D depiction of a 3d projection of a 4D cube. You could build a 3D wireframe for each frame of that animation, and wouldn't have a 4D cube.
Technically, a projective representation of a tesseract. There is no way to imagine/visualize a tesseract qua tesseract. But is it is a beautiful video!
I cannot imagine 4 Euclidean dimensions (I can define, but not imagine), but I have no problem modeling 4 dimensions in a volumetric model that can be embedded in Euclidean 3-space.
In fact, I imagine that even 5 and 6 dimensional geometric systems can and do exist within Euclidean 3-space. One must be careful identifying the concept "dimension" as a geometric concept, tying it to the presumed coordinate space; the proper notion of dimension is the order of the minimum set that spans the vector space of interest.
Euclidean 3-space is spanned by a set of three elements, if one presumes that any real number can be used as scaling coefficient. But in general, volumetric spaces are not Euclidean 3-spaces, despite the usual conflationary presumption that because Euclidean 3-space coordinates volumes, that volume must be identified with Euclidean 3-space. It is just not so.
In other words, Euclidean 3-space coordinates volume, but volume is not necessarily an Euclidean 3-space.
If you have an Euclidean 3-space, then you can coordinate volume.
The converse is not implied, it is not an if and only if statement, in principle. In other words, the statement does NOT imply the converse, i.e., the statement:
"If you can coordinate volume, then you must have an Euclidean 3-space."
Its in wiki da...
ReplyDeleteYou can post it on optical illusion community.
ReplyDeleteIt is a 4-dimension cube
ReplyDeleteNice Box...
ReplyDeletewow,very cool ....the 3d mutation cube
ReplyDeletesorry metatron cube
ReplyDeleteI know this is splitting hairs, but it's a 2D depiction of a 3d projection of a 4D cube. You could build a 3D wireframe for each frame of that animation, and wouldn't have a 4D cube.
ReplyDeleteAlanvaati Zhuvaati Braingasm?
ReplyDeleteStill awesomely beautiful though, of course.
ReplyDeleteScott Carter Great video
ReplyDeleteTechnically, a projective representation of a tesseract. There is no way to imagine/visualize a tesseract qua tesseract. But is it is a beautiful video!
ReplyDeleteDavid Chako Agreed
ReplyDeleteAlso called hypercube
ReplyDeletePretty good animation but what we'll really see in practice? I mean how one could recognize that it is a real hypercube in front of him?
ReplyDeleteNikolai Varankine U should let me know if u're able to see the 4th dimension with ur naked eye or at least share the secret :)
ReplyDeletehypercube....try tying it in a knot.
ReplyDeletepretty interesting actually.
ReplyDeleteCorina Marinescu , Sorry, I can't see 4th-D. At least I thought so. Before I read about quasicrystal discovery. http://en.wikipedia.org/wiki/Quasicrystal
ReplyDeleteI cannot imagine 4 Euclidean dimensions (I can define, but not imagine), but I have no problem modeling 4 dimensions in a volumetric model that can be embedded in Euclidean 3-space.
ReplyDeleteIn fact, I imagine that even 5 and 6 dimensional geometric systems can and do exist within Euclidean 3-space. One must be careful identifying the concept "dimension" as a geometric concept, tying it to the presumed coordinate space; the proper notion of dimension is the order of the minimum set that spans the vector space of interest.
ReplyDeleteEuclidean 3-space is spanned by a set of three elements, if one presumes that any real number can be used as scaling coefficient. But in general, volumetric spaces are not Euclidean 3-spaces, despite the usual conflationary presumption that because Euclidean 3-space coordinates volumes, that volume must be identified with Euclidean 3-space. It is just not so.
In other words, Euclidean 3-space coordinates volume, but volume is not necessarily an Euclidean 3-space.
ReplyDeleteIf you have an Euclidean 3-space, then you can coordinate volume.
The converse is not implied, it is not an if and only if statement, in principle. In other words, the statement does NOT imply the converse, i.e., the statement:
"If you can coordinate volume, then you must have an Euclidean 3-space."
is not implied, and is, in general, FALSE.
continous topology
ReplyDelete